| Abstract: | Ordinary differential equation (ODE) population models have been pivotal in the development of ecological theory. Here I propose an ODE formulation that is biologically more consistent than previous formulations and applies equally well to modeling predation, competition, mutualism, and combinations of all three in complex food webs. The formulation is based on two principles: I. The rate at which a population consumes resources is determined by a functional response that includes the effects of both consumer satiation and intraspecific interference competition; II. The intrinsic growth rate of a population, independent of trophic level, is a saturating function of resources consumed and approaches minus infinity as the rate of resources consumption approaches zero. After deriving a general model, I consider specific forms for the consumption and growth functions associated with Principles I and II. I use these functions to derive a generalized logistic growth model, in the process expressing the logistic growth and carrying capacity parameters in terms of the biologically more intuitive consumption and intrinsic growth function parameters. I then go on to consider specific prey-predator, trophic stack, consumer-resource, competition, and mutualism models and, where appropriate, contrast them with models that have been obtained by direct modification of the Lotka-Volterra approach to multispecies analysis. |
